Liberal MPs could get a free vote on same-sex marriage when the issue is put to a meeting in August.
A cross-party bill is expected to go to parliament on August 11, pending a decision by the selection committee.
Liberal Warren Entsch will move the bill and Labor MP Terri Butler will second it, under an agreement reached last week.
Mr Entsch and fellow Queensland Liberal Teresa Gambaro would then seek the support of their colleagues at a meeting on August 18 on allowing frontbenchers a free vote on the bill.
Ms Butler told AAP the law will be drafted in a way to ensure it had the best chance of gaining support.
While it's "slightly" different to Labor's bill introduced on June 1, it uses the same language to replace "man and woman" with the words "two people" in the Marriage Act.
A new clause will ensure that chaplains, as well as church ministers, won't be compelled to preside at same-sex marriages. However, all parties believe it will only succeed if Prime Minister Tony Abbott allows all Liberal MPs a free vote.
"I hope the fact there is a cross-party bill that can be owned by the entire parliament will help the Liberals and Nationals to do the right thing and support marriage equality," Ms Butler said.
"The ball is squarely in their court - they know where we stand."
A spokeswoman for Mr Abbott told AAP the PM remained opposed to same-sex marriage.
"Any member can introduce a private member's bill into the parliament but they do not come before the joint party room for discussion unless they will be voted on in the parliament," she said.
"It is rare for a private member's bill to be voted on and any bill would be subject to the usual process."
Opposition Leader Bill Shorten said in a statement he welcomed the move as a "sign of progress" and hoped Mr Abbott would allow a free vote.
The outcome was more important than whose name was on the bill, he said.
"Like millions of Australians, my first and only hope here is that we can make marriage equality a reality."
Liberal backbenchers can vote freely on such bills, but coalition policy to support only male-female marriage compels any senior members to quit their post if they want to cross the floor.
Mr Abbott had asked coalition supporters of the law change to hold fire until key budget measures were passed - which they have now done.
Two independents, Andrew Wilkie and Cathy McGowan have given their backing.
Ms McGowan said her Victorian regional electorate of Indi supports same-sex marriage.
A spokesman for Mr Entsch said the "issue needs to be approached in a careful, considered and respectful manner."
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